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Factoring Quadratic Trinomials

Updated on September 5, 2011

FACTORING QUADRATIC TRINOMIALS

One of the most important lessons in Algebra is factoring quadratic trinomials. In this hub I present some exercises with their solutions and techniques.


Exercise Number One : FactorX2 + 10X + 16

The factor of a quadratic trinomial are two binomials such that the first term of every binomial are the factorsof X2 and the second term of every binomial are the factors of 16.

Our factors are :(X + 8) (X + 2)

Before accepting this as a factor you have to test : Product of the outer terms plus the product of the inner terms must be equal to the middle term of the trinomial you are factoring.

Let us see:2X +8X= 10X

10X is the middle term of the trinomial therefore our factors are correct.


Exercise Number Two : FactorX2 + 3X – 28

We notice that the sign of the third term of the trinomial we are factoring is negative therefore the factors must be a positive and a negative number for opposite sign gives a negative product. We also notice that the sign of the middle term is positive therefore the product with a bigger absolute value must be positive.

Our factors are : (X + 7 ) (X – 4)

Outer product : -4X

Inner product also the product with a bigger absolute value: 7X

Let us see : 7X + -4X=3X

3X is the middle term of the trinomial therefore our factors are correct.


Exercise Number Three : Factor3X2 – 10XY – 8Y2

We notice that the sign of the middle term is negative therefore the product with a bigger absolute value must be negative.

Our factors :(3X + 2Y ) (X – 4Y)

Outer product also the product with a bigger absolute value : -12XY

Inner product : 2XY

-12XY + 2XY = -10XY

-10XY is the middle term of the trinomial therefore our factors are correct.


Exercise Number Four : Factor 4X2 -19X + 12

We notice that the sign of the third term of the trinomial we are factoring is positive while the sign of the middle term is negative. In this case the sign of both factors of the third term must be both negative to follow the rule that same sign gives positive product. They are both negative because the sign of the middle term is negative.

Our factor : (4X – 3) ( X – 4)

Outer product : (4X)(-4)= -16X

Inner product: ( X)(-3)= -3X

-16X + -3X= -19X

-19X is the middleterm of the trinomial we are factoring therefore our factors are correct.

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    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      7 years ago from Manila

      Hi carcro it is great to hear from you.Thank you for voting this hub up and useful. Thank you for dropping by and appreciating this hub. Your visit is greatly appreciated. Remain blessed always. Best regards.

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      7 years ago from Manila

      Hi kerlynb I am glad to hear from you. Thank you for gracing this hub. Your visit and comments are much appreciated. Blessings to you and best regards.

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      7 years ago from Manila

      Hi lord de cross thank you for dropping by and appreciating this hub. Your visit is always appreciated. Blessings to you and your family. Best regards.

    • carcro profile image

      Paul Cronin 

      7 years ago from Winnipeg

      I love math, always have. I wish they had really good tutorials like this when I was younger. Thanks for sharing...I can at least pass this along to my nephews and nieces! Voted Up and Useful!

    • kerlynb profile image

      kerlynb 

      7 years ago from Philippines, Southeast Asia, Earth ^_^

      Trinomials!?! :D It was so tough for me when I was younger :( Good thing I'm now done with school. Thanks for this hub though. Made me remember my school days with fondness.

    • Lord De Cross profile image

      Joseph De Cross 

      7 years ago from New York

      Hi Cristina,

      You brought me back so many memories. 4 examplas with enlough variety for our students to understand better. Thanks for taking your time in writing this hub.

      LORD

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